一类分数阶积分-微分Langevin方程初值问题解的存在唯一性  

Existence and uniqueness of solutions of initial value problems for fractional integro-differential Langevin equation

作　　者：李跃龙 郝新安[1] LI Yuelong;HAO Xin'an(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong,PRC)

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报（自然科学版）》2024年第4期22-28,共7页Journal of Qufu Normal University(Natural Science)

基　　金：山东省自然科学基金(ZR2022MA049).

摘　　要：该文研究含3个分数阶导数的非线性积分-微分Langevin方程初值问题.首先应用Schauder不动点定理得到了解的存在性结果,然后运用Banach压缩映射原理建立了解的唯一性,最后举例说明了主要结果的应用.In this paper,the solvability of initial value problems for fractional integro-differential Langevin equation involving three fractional orders is discussed.First,by means of Schauder fixed point theorem,an existence result for the solution is obtained.Then,the unique solution is established using the Banach contraction mapping principle.Finally,an example is provided to illustrate the main results.

关 键 词：分数阶Langevin方程 积分-微分方程 存在性和唯一性 不动点 

分 类 号：O175.14[理学—数学]